Doubly Fed Induction Generator Systems For Variable Speed Wind Turbine Rui Melício1, V.M.F. Mendes2 1
ISEL, DEEA, Secção de Economia e Gestão Rua Conselheiro Emídio Navarro, 1, 1950-062 Lisboa (Portugal). e-mail:
[email protected] 2
ISEL, DEEA, Secção de Economia e Gestão Rua Conselheiro Emídio Navarro, 1, 1950-062 Lisboa (Portugal). e-mail:
[email protected]
Abstract. This paper presents results of a study concerning the dynamic behaviour of a wind energy system powered by a doubly fed induction generator with the rotor connected to the electric network through an AC-AC converter. A tendency to put up more and more wind turbines can be observed all over the world. Also, there is awareness in taking into account the requirements of a clean environment, due to the need to preserve our habitat. Renewable energy sources not contributing to the enhanced greenhouse effect, specially wind power, are becoming an important component of the total generation. Hence, research concerning the dynamic behaviour of wind energy systems is important to achieve a better knowledge. Key words Wind energy, Wind turbine, doubly fed induction generator, AC-AC converter.
1. Introduction Wind energy continues to move forward in Europe, following Directive 2001/77/CE. States and customers are interested in providing the needed energy, taking into account the requirements of a clean environment. Renewable energy sources not contributing to the enhanced greenhouse effect, particularly wind power, are becoming an important component of the total mix generation. Wind Energy Conversion Systems, WECS, research has focused in wind power autonomous systems and gridconnected systems. An autonomous system directly supplies electricity to customers and it is especially appealing in areas with poor accessibility conditions for transmission lines, but autonomous system wind power generation should be complemented with other sources of power, because wind is an unpredictable energy source. Hence, it does not ensure continuous power supply. While, a gridconnected system have the advantage of ensuring continuous power supply, because when wind energy is insufficient the electrical grid satisfy the demand. A comparison between the variable speed wind turbine and the constant speed wind turbine [1] shows that variable speed reduce mechanical stresses: gusts of wind can be absorbed, dynamically compensate for torque and power pulsations caused by back pressure of the tower. This backpressure causes noticeable torque pulsations at
a rate equal to the turbine rotor speed times the number of rotor wings. The used of a doubly fed induction generator in WECS with the rotor connected to the electric network through an AC-AC converter offers the following advantages: • •
only the electric power injected by the rotor needs to be handled by the convert [1], implying a less cost AC-AC converter; improved system efficiency and power factor control can be implemented at lower cost, the converter has to provide only excitation energy [2].
Hence, taking advantage of power electronic advances in recent years, WECS equipped with doubly fed induction generator systems for variable speed wind turbine are one of the most efficient configurations for wind energy conversion. Portugal is expected until 2010 to have 3750 MW of wind power due to government resolution 63/2003. (Table I) shows data for the wind power capacity installed and in the construction phase in Portugal, Madeira and Azores at December 2004 [3]. Hydro power in Portugal accounts for about 20.25% in an average year. While, wind energy accounts for about 1.7% of the total energy consumed in Portugal. This total figure is still too far from the established goal of 39% of the total energy produced in accordance with the Directive 2001/77/CE. Table I. - Wind power, December 2004. WECS
Portugal Madeira Azores Total
Cons.(MW)
746.0
0.0
1.8
747.8
Inst. (MW)
505.5
9.6
5.3
520.4
Portugal WECS’s are grid-connected systems and the last year statistic shows that doubly fed induction generator systems are the option preferred for the WECS recently installed and in construction phase. This paper presents results of a study concerning the dynamic behaviour of a wind energy system powered by a doubly fed induction generator. Which is the actual preferred configuration for WECS in Portugal, due to the advantages.
We choose for the case study a WECS illustrated in (Fig. 1), composed by a grid-connected system with a variable speed doubly fed induction generator.
angle and is computed by the following nonlinear mathematical programming ⎛1 ⎞ −18.4 c p (0, λi )max = max 110.23 ⎜ − 0.11976 ⎟ e ⎝λ ⎠ s.t λ≥0
giving c p (0, λi )max = 0.4412 for λopt = 6.9
Fig. 1. Doubly fed induction generator WECS.
The system is equipped with controllers namely: pitch controller, speed controller and voltage controller.
2. Formulation The turbine model is based on the following: the mechanical power of the turbine is given by Pm =
1 ρ π D 2 v 3c p (β , λi ) 8
(1)
where ρ is the air density, D is the diameter of the blades, v is the wind speed, c p is the power coefficient [4], we consider it given by
where
⎛ 151 ⎞ c p (β , λi ) = 0.73 ⎜⎜ − 0.002 β − 13.2 ⎟⎟ e ⎝ λi ⎠ 1 λi = 1 0.035 − (λ + 0.08 β ) β 3 + 1
(
λ=
and
−18.4 λi
1 Dωr 2 v
(2)
λ is the tip speed ratio, β is the pitch angle of rotor blades, ω m is the mechanical angular speed. The power coefficient in (2), is shown in (Fig.2) as function of the tip speed ratio parameterised in function of the pitch angle.
Power coefficient
0.5 0.4
10º
0.2
15º
0.1
0
2
4
dλqs dt = u qs − Rs iqs − ω λds
dλdr dt = u dr − Rr idr + sω λqr
(5)
λds = Ls ids + M idr
25º
0
dλds dt = u ds − Rs ids + ω λqs
The stator electric values are indicated by the subscript s and the rotor electric values are indicated by the subscript r. u is a voltage, R is a resistance, i is a current, λ is a flux linkage. ω is the stator electrical frequency and s is the rotor slip. The flux linkages are given by
5º
0.3
(4)
where J is the moment of inertia due to the rotating mass and Pa is the rotor accelerate mechanical power. The angular velocity of the rotor is considered in the region 0.7 ω ≤ ω r ≤ 1.3ω for the case study. The doubly fed induction generator equations, using the motor convention, are the following
dλqr dt = u qr − Rr iqr − sω λdr
0º 2º
(3)
This value for the power coefficient is used for wind speed not greater than the nominal wind speed for the turbine. Pitch angle control operates only when the value for wind speed is greater than the nominal wind speed. Half of the world’s leading wind turbine manufacturers use the doubly fed induction generator systems. This is due to the fact that the power electronic converter only has to handle a fraction (20% – 30%) of the total power, i.e., the slip power. This means that if the speed is in the range ±30% around the synchronous speed, the converter has a rating of 30% of the rated turbine power, reducing the losses in the power electronic converter, compared to a system where the converter has to handle the total power. In addition, the cost of the converter becomes lower [1]. The doubly fed induction generator has been used in wind turbines for a long time. In the past, the ACAC converter connected to the rotor consisted of a rectifier and inverter based on thyristor bridges [5]. Nowadays, AC-AC converters are equipped with bidirectional IGBT's [2], connecting the rotor of the variable speed doubly fed induction generator to the electrical grid. The equation of rotor motion is given by
dω r dt = 2 Pa ( Jω r )
)
(1/ λ − 0.003)
6
8
10
12
Tip speed ratio
λqs = Ls iqs + M iqr
λdr = Lr idr + M ids
Fig. 2. Power coefficient.
λqr = Lr iqr + M iqs
At lower wind speed, the pitch angle is null. The maximum power coefficient is given for a null pitch
Ls , Lr and M are respectively the stator and the rotor leakage inductance and the mutual inductance between
(6)
the stator and the rotor. The stator and rotor active and reactive are given by
In Figure 5 and Figure 6, we observe the stator power and the rotor power.
Ps = 3 2 (u ds ids + u qs iqs )
Pr = 3 2 (u dr idr + u qr iqr )
Qs = 3 2 (u ds iqs − u qs ids ) Qr = 3 2 (u dr iqr − u qr idr )
(7)
The rotor accelerate mechanical power, the rotor electric power and the stator electric power [6], are given by Pa = Ps − Pm − Pr
Pr = Pm [ s (1 − s )] Ps = Pm [1 (1 − s )]
(8)
Fig. 5. Stator power.
neglecting the copper losses in the rotor and the stator.
3. Case study The main objective of the simulations is to evaluate the behaviour of the doubly fed induction generator system due to gusts of wind. The nominal power of the wind turbine is 850 kW. The nominal wind speed for the turbine is 11.4 m/s. We consider the wind speed change as shown in (Fig. 3). Fig. 6. Rotor power.
In Figures 7, we observe the output power.
Fig. 3. Wind speed.
The mechanical power due to the wind speed change is shown in (Fig. 4). Fig. 7. Output power.
In (Figures 8 and 9), we observe the angle set point and the corresponding pitch angle increase in order to limit the excursion of the mechanical power to return to normal power condition.
Fig. 4. Mechanical power.
The increase in the wind speed implies that the mechanical power has tendency to be greater than the nominal power, but owing to the pitch angle control the mechanical power excursion is limited. The decrease in the wind speed reduces the mechanical power and the pitch angle control returns to a null pitch angle.
Fig. 8. Set point angle.
to the electrical network through an AC-AC converter, improving the efficiency of the power conversion.
References
Fig. 9. Pitch angle.
In (Figures 10 and 11), we observe that the rotor speed and the rotor slip.
Fig. 10. Rotor speed.
Fig. 11. Rotor slip.
After the wind speed returned to the value less the nominal wind speed for the turbine, returns to the normal operation value, the pitch angle returns (see Fig. 9) to normal operation value.
4. Conclusions Wind energy continues to move forward in Europe and deregulation provides an opportunity for investments in WECS. Hence, it is expected that wind power will be a significant component of the total generation mix in the near future. Due to the advances in power electronics it is possible to use the doubly fed induction generator system with variable speed connected
[1] PETERSON ANDREAS, HARNEFORS LENNART and THIRINGER TORBJÖRN, “Evaluation of Current Control Methods for Wind Turbines Using Double-Fed Induction Machines”, IEEE Trans. On Power Electronics, Vol. 20, No. 1, pp 227-235, January 2005. [2] MÜLLER, S.; DEICKE, M.; DE DONCKER, RIK W. “Doubly Fed Induction Generator Systems for Wind Turbines”, IEEE Industry Applications Magazine, Maio / Junho de 2002. [3] INEGI, Parques Eólicos em Portugal, Dezembro de 2004. [4] SLOOTWEG, J. G.; HAAN, S. W. H.; POLINDER H.; KLING, W. L. (2003) General Model for Representing Variable Speed Wind Turbines in Power System Dynamics Simulations. IEEE Trans. on Power Systems, vol. 18, Nº 1, February. [5] SLOOTWEG, J. G.; POLINDER H.; KLING, W. L. (2001) Dynamic Modelling of a Wind Turbine witf Doubly Fed Induction Generator. IEEE Trans. on Power Systems. [6] SIMÕES, M. GODOY; FARRET, FELIX A., Renewable Energy Systems, CRC Press, Boca Raton Florida (2004).
